Cover eggs with 1 inch water in a saucepan; bring to a full boil.

Cover; remove from heat and rest 12 minutes until yolks fully set.

Chill in ice water 5 minutes; peel and chop into 1/3-inch pieces.

Fold with mayonnaise, pickles, celery, Dijon, salt, and pepper, retaining white texture.

Chill 20 minutes; divide over 4 bread slices and top each with lettuce.

Close with remaining bread; halve.